Supporting vectors vs. principal components
Metadatos
Afficher la notice complèteEditorial
AIMS
Materia
Bounded linear operator Hilbert space Mean operator Principal components Supporting vector
Date
2022-10-26Referencia bibliográfica
Almudena P. Márquez... [et al.]. Supporting vectors vs. principal components[J]. AIMS Mathematics, 2023, 8(1): 1937-1958. doi: [10.3934/math.2023100]
Patrocinador
Spanish Government FEDER-UCA18-105867; ERDF Operational Programme; University of the Regional Government of Andalusia PGC-101514-B-I00Résumé
Let T : X -> Y be a bounded linear operator between Banach spaces X, Y. A vector x(0) is an element of S-X in the unit sphere S-X of X is called a supporting vector of T provided that parallel to T(x(0))parallel to = sup{parallel to T(x)parallel to : parallel to x parallel to = 1} = parallel to T parallel to. Since matrices induce linear operators between finite-dimensional Hilbert spaces, we can consider their supporting vectors. In this manuscript, we unveil the relationship between the principal components of a matrix and its supporting vectors. Applications of our results to real-life problems are provided.